Question

Multiple choice:
I have a choice of two routes to get to work. The probability that I choose the first route on
any day is 0.6, and the probabilities of my being delayed on the journey are 0.1 for the first
route and 0.2 for the second. Calculate the probability of my being delayed exactly once in
three days.
A to E:
0.05/0.31/0.4/0.54/0.86

Answer 1

First you need to find the probability of a delay on any day. This can be done by drawing a probability tree. Can you do that?

Answer 2

From the above probability tree you can find the total probability of a delay on any day as:
\[P(delay\ on\ any\ day)=(0.6\times0.1)+(0.4\times0.2)=you\ can\ calculate\]
When you have done the calculation, please post the result. Then we can find the required probability by using the binomial distribution.

Answer 3

@skscjswo373 Are you there?

Answer 4

Oh sorry, so it is 014. I have actuly calculated until here, but after that, I am sure what to do.. Do I need to use Binomial? How can I deal with 3 days??

Answer 5

Using the binomial distribution we get:
\[P(1\ delay\ out\ of\ 3\ days)=\left(\begin{matrix}3 \\ 1\end{matrix}\right)0.14\times(0.86)^{2}=3\times0.14\times(0.86)^{2}=you\ can\ calculate\]

Answer 6

Oh yeah! Thank you so much!

Answer 7

You're welcome :)